The versine formula and its limitations

Where the author eloquently discusses the versine formula and the accuracy loss implied by ignoring a historically insignificant term of its equation, demonstrates an easily replicable CAD check of this inaccuracy, and reveals the EXACT versine formula.

snippet – Track realignment using involutes

Hallade was not alone. His method of track alignment rectification is by far the most used and known but there are quite few other methods for rectification and even proper realignment. One of these methods used a strange curve called involute (or evolvent). It was first described in this book from 1927. Die Absteckung von…